Others have already answered yes and several have offered up lightness
and speedplay (presumeably because of float) as road options. I also
use SPD pedals- WTB 250 "Stealth" in my case. They are quite cheap (I
haven't paid more than $50 off ebay or on-line), light and offer
adjustable float. Bebop are another option but they are more
expensive.

I will need to buy pedals for the bike.
I already own a pair of SPD-mountain bike shoes and I am cheap.
Will I be able to mount mountain bike pedals on this bike?
Is there any reason not to?